TFS · Practice Exam 1 · Problem 23PDFSolution in PDF ↓
TFS · Practice Exam 1 · Problem 23
Problem & Solution
Video Synthesis
- Problem: In a steam heat exchanger, 750 pounds per hour, a 500-degree steam at atmospheric pressure is used to heat 80 gpm of cold water, initially at 50 degrees.
- Approach: If the steam exits as a saturated liquid, what is the final temperature of the water, assuming there are no losses?
- Key values: 80 gpm, 14.7 psi
- Reference: steam table, reference handbook
- Result: And since it's heating, T4 is going to be greater than T3 so that equals T4 minus T3.
- ✅ Answer: C
Office Hours
2
Student questions asked in live office hours about this problem
OH 52
Q: Why cannot we use the PHFG (enthalpy of vaporization) for 500°F steam entering a heat exchanger at 1 ATM, when the heat loss is due to state conversion from steam to saturated water?
A: The steam at 500°F and 1 ATM is superheated, not saturated—since the saturation temperature at 1 ATM is only 212°F. The steam must first cool at constant pressure to become saturated vapor, then condense; the sensible cooling portion gives up significant heat beyond just the phase change, so using only HFG (which represents only the condensation) misses a substantial portion of the total heat transfer.
OH 61
Q: If GPM wasn't given on the water side, could you still use Q_water = m_dot × ΔH equal to the steam side instead of the 500 GPM × ΔT rule of thumb?
A: Yes, you have options depending on what information is given. You can use m_dot × ΔH for the water side if you have mass flow rate instead of volumetric flow rate, or m × cp × ΔT for sensible heating at constant pressure. These approaches are interchangeable since mass flow rate equals density times volume flow rate, so you should be able to convert between them.